Search results for "group theory"
showing 3 items of 703 documents
Multiparametric Rational Solutions of Order N to the KPI Equation and the Explicit Case of Order 3
2021
We present multiparametric rational solutions to the Kadomtsev-Petviashvili equation (KPI). These solutions of order N depend on 2N − 2 real parameters. Explicit expressions of the solutions at order 3 are given. They can be expressed as a quotient of a polynomial of degree 2N(N +1)−2 in x, y and t by a polynomial of degree 2N(N +1) in x, y and t, depending on 2N − 2 real parameters. We study the patterns of their modulus in the (x,y) plane for different values of time t and parameters.
Higher-order Nonnegative CANDECOMP/PARAFAC Tensor Decomposition Using Proximal Algorithm
2019
Tensor decomposition is a powerful tool for analyzing multiway data. Nowadays, with the fast development of multisensor technology, more and more data appear in higherorder (order > 4) and nonnegative form. However, the decomposition of higher-order nonnegative tensor suffers from poor convergence and low speed. In this study, we propose a new nonnegative CANDECOM/PARAFAC (NCP) model using proximal algorithm. The block principal pivoting method in alternating nonnegative least squares (ANLS) framework is employed to minimize the objective function. Our method can guarantee the convergence and accelerate the computation. The results of experiments on both synthetic and real data demonstrate …
The link of a finitely determined map germ from R 2 to R 2
2010
Let f: (R2, 0) → (R2, 0) be a finitely determined map germ. The link of f is obtained by taking a small enough representative f: U ⊂ R2 → R2 and the intersection of its image with a small enough sphere Sε1 centered at the origin in R2. We will describe the topology of f in terms of the Gauss word associated to its link.